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arXiv · 1010.1811

Fano type quantum inequalities in terms of $q$-entropies

Alexey E. Rastegin
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Abstract

Generalizations of the quantum Fano inequality are considered. The notion of $q$-entropy exchange is introduced. This quantity is concave in each of its two arguments. For $q\geq0$, the inequality of Fano type with $q$-entropic functionals is established. The notion of coherent information and the perfect reversibility of a quantum operation are discussed in the context of $q$-entropies. By the monotonicity property, the lower bound of Pinsker type in terms of the trace norm distance is obtained for the Tsallis relative $q$-entropy of order $q=1/2$. For $0\leq{q}\leq2$, Fano type quantum inequalities with freely variable parameters are obtained.

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Alexey E. Rastegin. 2011-09-24. Fano type quantum inequalities in terms of $q$-entropies. https://arxiv.org/abs/1010.1811

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